The effective cross section area, or tensile area, of the external thread.

The shear area of the external thread which depends upon minor diameter of the tapped hole

The shear area of the internal thread which depends on the major diameter of the external thread

The allowable stresses and screw end force and the method of applying the force in the calculation
of the tensile stress are not considered on this page but are addressed on this site by tables
and more importantly referenced links

If a screw threaded fastener is to fail it is preferable that the screw fails rather than the internal
or external thread strips. The length of the screw engagement should therefore be sufficient to carry
the full load necessary to break the screw without the threads stripping.

The size of a screwed fastener is first established by calculating the tensile
load to be withstood by the screw and selecting a suitable screw to withstand the tensile load
with the appropriate factor of safety or preload. If the joint is fixed using
a nut and bolt then assuming the nut is selected from the same
grade as the bolt there is little need to size the nut. The fastener manufacture
sizes the length of the nut to ensure the screw will fail before the nut. If the screw fastens
into a tapped hole then a check of the depth of thread engagement is required.

Generally for female and male threads of the same material with, the female thread is stronger
than the male thread in shear for the same length of engagement

The following rules of thumb are suggested for arriving at reasonable lengths of thread for steel screws used with screwed holes in weaker materials.

For steel a length of thread engagement of at least 1 x Nominal dia's of the thread
For Cast Iron or brass or bronze the thread engagement should be at least 1,5 x Nominal dia's of the thread
For Aluminium , zinc or plastices the thread engagement should be at least 2 x Nominal dia's of the thread

However for a quality safe connection, when the tapped material has a significantly lower ultimate tensile strength than the screw material,
- to ensure the screw will fail in tension before the female, it is preferable to use suitably rated nuts or engineered thread inserts.

Various studies on thread loading have established that
the shear stress is not evenly distributed across the threads. The first thread withstanding the load
is the highest stressed and the next one is much less stressed and so on... . If the thread materials were
very hard and did not yield the first thread could be withstanding nearly all
the load. However because of material yielding there is some distribution
of the load. A study (see link 2 below) has established that for a typical grade 8 nut the percentage
of the load taken by consecutive threads are about 34%, 23%, 16%,11%,9%, 7% .... This effect can be alleviated
by using very accurate threads and by using ductile materials for the components. It has been established that,for carbon steel,
there is no increase in thread shear strength by having a thread engagement length in excess of the screw diameter.
It is normal practice to use a tapped hole depth of about 1,5 x nominal diameter - this allows at least 1 diameter of good thread engagement.

A very simple rule that can be applied for that vast majority of applications is that a thread length of 80% of the
screw diameter (standard nut height) is sufficient for ensuring that the screw will fail in tension before the female thread (nut) fails in
thread stripping (assuming the screw and nut are similar materials). Equations below indicate how to make adjustments if
the tapped metal (nut) strength is lower than the screw/bolt.

To ensure that the screw fails before the thread strips it is necessary the
the shear area is at least 2 times the tensile area. i.e

Le (min) = 2 . A t / [0.5 .π.(D - 0.64952.p )]

This assumes that the male and female thread materials have the same strength.
If the Female Material strength is lower i.e J as calculated below is greater than 1 then the length of engagement must be increased to prevent the female
thread stripping

If the value of J is greater than than 1 then the length of engagement must be increased
to at least

More Detailed Notes

The above formulae are sufficient to enable the tensile strength to be calculated
and to allow the depth of thread to be confirmed for a tapped hole

Following are equations to provide more accurate evaluation of the shear strength of
threads. These are equations derived from FED-STD-H28/2B, 1991 and Machinerys Handbook
eighteenth Edition. They strictly apply to UN thread series but if the relevent
metric screw thread dimensions are used they will give reasonable results. In practice
when the values are calculated the value for the screw shear strength is similar to the very
convenient formula provided above. These equations are only of theoretical value

The purpose of this table is to show the results of the above formula. It is
clear from this table that there is no major benefit in using the detailed formula
above. The approximate formula for the screw thread shear stress area
(A ss) is generally sufficiently accurate and there is no need to use
the more detailed formula for As. For sizes below M6 the formulas yield
very similar values. For sizes M6 and above the value for Ass provides a slightly more
conservative result (20% margin at M36)

I have obtained the thread dimensions on tables in Machinery's Handbook 27th ed. If you intend to
use this information please check it against a reliable source (ref disclaimer above)

All dimensions in mm

Size

M3

M4

M5

M6

M8

M10

M12

M14

M16

M20

M22

M24

M30

M36

Basic Dia

D (mm)

3.00

4.00

5.00

6.00

8.00

10.00

12.00

14.00

16.00

20.00

22.00

24.00

30.00

36.00

Pitch

p

0.50

0.70

0.80

1.00

1.25

1.50

1.75

2.00

2.00

2.50

2.50

3.00

3.50

4.00

1/p

n

2.0000

1.4286

1.2500

1.0000

0.8000

0.6667

0.5714

0.5000

0.5000

0.4000

0.4000

0.3333

0.2857

0.2500

Stress Dia

D s

2.5309

3.3433

4.2494

5.0618

6.8273

8.5927

10.3582

12.1236

14.1236

17.6545

19.6545

21.1854

26.7163

32.2472

Tensile Stress Area

A t

5.0308

8.7787

14.1825

20.1234

36.6085

57.9896

84.2665

115.4394

156.6684

244.7944

303.3993

352.5039

560.5872

816.7226

Pitch circle dia.

d p

2.6752

3.5453

4.4804

5.3505

7.1881

9.0257

10.8633

12.7010

14.7010

18.3762

20.3762

22.0514

27.7267

33.4019

Approximate Method

Shear Area/unit Length

Ass/mm

4.2023

5.5690

7.0378

8.4045

11.2910

14.1776

17.0641

19.9506

23.0922

28.8653

32.0069

34.6383

43.5530

52.4676

Shear Area

Assm
=2. At

10.0616

17.5574

28.3650

40.2468

73.217

115.9792

168.533

230.8788

313.33568

489.5888

606.7986

705.078

1121.1744

1633.4452

Length of Thread (Ass=2*At)

Le = Ass /A ss/mm

2.3944

3.1527

4.0304

4.7887

6.4845

8.1805

9.8765

11.5725

13.5689

16.9612

18.9584

20.3534

25.7428

31.1324

More Accurate Method

Max.Minor Dia (nut)

Knmax

2.5990

3.4220

4.3340

5.1530

6.9120

8.6760

10.4410

12.2100

14.2100

17.7440

19.7440

21.2520

26.7710

32.2700

Min Pitch Dia (Screw)

E smin

2.5800

3.4330

4.3610

5.2120

7.0420

8.8620

10.6790

12.5030

14.5030

18.1640

20.1640

21.8030

27.4620

33.1180

Max Pitch dia (Nut)

E sub>nmax

2.7750

3.6630

4.6050

5.5000

7.3480

9.2060

11.0630

12.9130

14.9130

18.6000

20.6000

22.3160

28.0070

33.7020

Min Major dia (Screw)

D smin

2.8740

3.8380

4.8260

5.7940

7.7600

9.7320

11.7010

13.6820

15.6820

19.6230

21.6230

23.5770

29.5220

35.4650

Shear Area/unit length (Screw)

A s /mm

3.9034

5.4728

7.0731

8.6458

12.1612

15.5796

18.9762

22.4239

26.0969

33.2791

37.0302

40.4623

51.6384

63.0982

Shear Area /mm length (Nut)

A n/mm

5.5466

7.7691

9.9988

12.1909

16.8285

21.4769

26.1173

31.0335

35.5699

45.3881

50.0141

55.0098

69.5512

84.0601

Length of Thread (As= 2*At)

Le

2.5777

3.2081

4.0103

4.6551

6.0206

7.4443

8.8813

10.2961

12.0067

14.7116

16.3866

17.4238

21.7120

25.8873

Relevant Links

Bolt Science..A site dedicated to the Science & Technology of bolted joints